# Teaching Resources

During the fall of 2013, we began developing a number of active learning tutorials for use in introductory and advanced physics classes. We are making them available for anyone to use. We would appreciate knowing that you are using them and would appreciate receiving any feedback (good/bad/neutral/suggestions/etc.). Contact Drew Milsom at milsom@email.arizona.edu

At the end of each file is a section describing how students have performed on each of the questions (basically advice to help manage the activity better and/or to better train your learning assistants), a section keeping track of modifications and a section giving the source of the material (original, modified version of XXX, etc.)

The development of some of this was supported by the Association of American Universities under Grant #4209930 and support was also provided by both the Physics Department and the College of Science at the University of Arizona.

**USAGE GUIDELINES:**

Please do not write detailed solutions to these tutorials and provide them to your class. We do not want answers all over the internet. We have a set of solutions (basically final answers and several sentence answers to some conceptual questions) which you can ask for (email milsom@email.arizona.edu). We do post these for students (although admittedly most students never look at them).

**HOW WE USE THESE IN CLASS:**

Our primary use of these is during one day per week when our classes meet in a “collaborative classroom” on campus. These rooms are filled with small tables. The students work in groups of four. At the end of the 50 minutes, we collect the work of ONE student at each table and all four students will get the same grade. This helps encourage collaboration.

We always give them more to work on than they will get done since we don’t want anyone leaving early. We tell them that they can finish anything else on their own since it will be good practice and that we are happy to discuss any of the questions during office hours. (Again, please do not post detailed solutions to the questions).

Some of the activities involve a guided solution to a standard homework problem. For example Calculating the electric field using the integral form of Coulomb’s Law is clearly meant to take the entire period and help them develop the skills necessary to solve a similar problem on their own.

Others are really a collection of much shorter activities. For example, the Linear Momentum tutorial is really five separate activities. We often hand out one of these shorter activities during our standard “lectures”. It is very useful to intersperse these into the lecture so you can immediately assess their understanding of what you just discussed.

**WE HAVE TUTORIALS FOR THE FOLLOWING SUBJECTS:**

These activities cover the topics in your standard mechanics class: kinematics, Newton's laws and dynamics, conservation laws, rotation, simple harmonic motion, fluids and gravitational fields. Some of the tutorials can be used in either algebra-based or calculus-based courses while others are specifically for the algebra-based courses (and the file name will tell you that).

Samples:

- Circular motion and centripetal acceleration
- Newton's laws: Pulling a box at an angle
- A sphere rolling uphill

Download all Introductory Mechanics tutorials.

These activities cover the topics in your standard introductory electromagnetism class: electric forces and fields, electric potentials, AC and DC circuits with resistors, capacitors and inductors, magnetic forces and fields, Gauss’ Law, Ampere’s Law, Faraday’s Law and electromagnetic waves. Some of the activities can be used in either algebra-based or calculus-based classes while some of them clearly involve topics with lots of calculus.

Samples:

Download all Introductory Electromagnetism tutorials.

At this time, there are three tutorials focusing on geometric optics and three covering wave optics. All of the tutorials were written for an algebra-based physics course but could certainly be used in any introductory course.

Download all Optics tutorials.

We have five tutorials here covering heat capacities and specific heats, thermal expansion, phase changes, the First Law of Thermodynamics, typical thermodynamic processes and heat engines and refrigerators. These were all initially written for an algebra-based physics course but they would certainly be useful in any introductory course. Additional (and perhaps more advanced) tutorials may be added later.

Download all Thermodynamics tutorials.

These activities cover the topics in a typical two-semester sequence of advanced electromagnetism. While this may vary from university to university, the first half of our class covers approximately the first 21 chapters of Electromagnetic Fields by Roald K. Wangsness or equivalently the first seven chapters of Introduction to Electrodynamics by David J. Griffiths. Here are two samples which you can look at (one from each semester of the course):

Download all of the tutorials for each semester of the course:

During our classes here, we also use some resources developed at the University of Colorado that you may want to check out.

These activities cover topics from the first semester of a quantum mechanics class. Specifically, there are tutorials covering the following topics:

- Superposition States for a Particle in an Infinite Square-well.
- A Particle in a Ring.
- Ladder Operators for the Simple Harmonic Oscillator.
- Quantum Mechanics Jeopardy – Here is the Wavefunction. What is the Potential?

Download all Quantum Mechanics tutorials

Quantum Mechanics is the one upper-division subject with lots of resources available. We also use materials developed at:

- The University of Colorado: https://www.colorado.edu/per/resources/course-materials
- The University of Pittsburgh: https://sites.google.com/site/quiltbeta/
- The University of Washington: http://depts.washington.edu/uwpeg/tutorials-QM

Our Mathematical Methods course is typically taken by students in their fourth semester. It covers a very wide range of topics:

- Series Expansions
- Probabilities and Probabilities Distributions
- Complex Numbers
- Linear Algebra and Eigenvalues
- Fourier Series and Transforms
- Vector Operators and Coordinate Transformations and
- Partial Differential Equations

The activities found here are basically group problem-solving activities for all of these topics. They are meant to be used after the material has been covered in class.

Download all Intermediate Mathematical Methods tutorials.

At this time, there are three tutorials covering the Bohr atom, the solar proton-proton cycle and the photoelectric effect. All of these were written for an algebra-based physics course. We anticipate adding more tutorials in the future.

Download all Modern Physics tutorials.

These activities cover topics from your typical junior-level classical mechanics class. Specifically, there are tutorials covering the following topics:

- Some interesting features of projectile motion
- Critically damped oscillators
- Gravitational potentials and fields
- A multi-week activity covering Lagrangians and Lagrange Multipliers
- Central force motion
- Coriolis force

Download all Classical Mechanics tutorials.

This is a QUALITATIVE activity covering the famous brachistochrone problem. It can be used as a challenging exercise for freshmen and it helps them review approximately the first half of their mechanics course. It can also be used in a typical junior-level Lagrangian mechanics course as a prelude to obtaining the quantitative solution. Since it can be used in multiple classes, we have put it here separately.

Download the Brachistochrone tutorial.